This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're right to think about that! Yes, it will still give the same answer. Here's why: When you have a constant factor inside an integral, you can move it outside the integral sign. So, (1)/(2) · 2x (2x) \, dx is equivalent to (1)/(2) 2x (2x) \, dx. Let's re-examine the term from Step 1 of problem 4: v \, du = ((1)/(2)(2x)) (2x \, dx) This is a product of three terms: (1)/(2), (2x), and 2x. You can rearrange and factor out constants: (1)/(2) · 2x (2x) \, dx = x (2x) \, dx Or, if you prefer to keep the (1)/(2) and 2 separate initially: (1)/(2) · 2x (2x) \, dx = (1)/(2) 2x (2x) \, dx When you then integrate 2x (2x) and multiply by (1)/(2), you will arrive at the same result as integrating x (2x) directly. It's just a different way of grouping the constants, but the mathematical outcome remains identical. What's next? Send 'em! 📸